Quest for the Donor Star in the Magnetic Precataclysmic Variable V1082 Sgr

G. Tovmassian1 , J. F. González2,3, M.-S. Hernández4, D. González–Buitrago5, S. Zharikov1, and J. V. Hernández Santisteban61 Instituto de Astronomía, Universidad Nacional Autónoma de México, Apartado Postal 877, Ensenada, Baja California, 22800, México; gag@astro.unam.mx

2 Universidad Nacional de San Juan, Av. J. I. de la Roza 590 oeste, 5400 Rivadavia, San Juan, Argentina3 ICATE, CONICET, Av. España 1512 sur, J5402DSP San Juan, Argentina

4 Instituto de Física y Astronomía, Facultad de Ciencias, Universidad de Valparaíso, Av. Gran Bretaña 1111 Valparaíso, Chile5 Department of Physics and Astronomy, 4129 Frederick Reines Hall, University of California, Irvine, CA 92697-4575, USA

6 Anton Pannekoek Institute for Astronomy, University of Amsterdam, Science Park 904, NL-1098 XH Amsterdam, The NetherlandsReceived 2018 May 8; revised 2018 October 24; accepted 2018 October 24; published 2018 December 7

Abstract

We obtained high-resolution spectra and multicolor photometry of V1082 Sgr to study the donor star in this 20.8 hrorbital period binary, which is assumed to be a detached system. We measured the rotational velocity( = v isin 26.5 2.0 km s−1), which, coupled with the constraints on the white dwarf mass from the X-rayspectroscopy, leads to the conclusion that the donor star barely fills 70% of its corresponding Roche lobe radius. Itappears to be a slightly evolved K2-type star. This conclusion was further supported by a recently publisheddistance to the binary system measured by the Gaia mission. At the same time, it becomes difficult to explain avery high (>10−9 -

M yr 1) mass transfer and mass accretion rate in a detached binary via stellar wind andmagnetic coupling.

Key words: binaries: close – novae, cataclysmic variables – stars: individual (V1082 Sgr) – star: rotation – stars:winds, outflows

1. Introduction

The term magnetic pre-polars was coined by Schwope et al.(2009), when it was recognized that some magnetic whitedwarfs (MWDs) are accreting matter from the secondary, anactive late-type main-sequence star underfilling its Roche lobe.The spectra of these systems show strong cyclotron harmonicsin the form of wide humps superimposed on the WD+M-dwarfstellar continuum. Accretion onto the MWD primary is of theorder of 10−14

–10−13 -M yr 1, comparable to what is expected

from the wind of a chromospherically active companion star(Schwope et al. 2002). Ferrario et al. (2015) listed 10 suchsystems, all of which contain M dwarfs as a donor star. It isnatural to assume that there also should exist pre-polars withdonor stars of earlier spectral types. It is not clear how justifiedthe term pre-polars would be for wider systems with earlier-type companions. But let us assume that pre-polars aredetached binaries consisting of a strongly MWD and anylate-type zero-age main-sequence (or nearly so) magneticallyactive star, in which the magnetic fields are coupled, forcingsynchronous rotation of the components and driving masstransfer. Observationally, pre-polars with earlier-type compa-nions might manifest themselves differently than thosecontaining an M dwarf.

Tovmassian et al. (2016, 2017) proposed two candidates forpre-polars with early-K companions. One of them is V1082 Sgr,remarkable for its cyclical accretion activity and low-luminosityepisodes during which the K star is the predominant sourceof light. V1082 Sgr is a prominent X-ray source. Bernardiniet al. (2013) studied it with several available X-ray telescopesand concluded that it is a highly variable X-ray source witha spectrum matching those of magnetic cataclysmic variables(CVs). They identify a small X-ray-emitting region where theplasma has typical temperatures achieved in a magneticallyconfined accretion flow. Using the model of Suleimanov et al.(2005), the mass of the magnetically accreting WD wasestimated to be Mwd=0.64±0.04M. From the derived WD

mass and radius (8.3×108 cm), they deduced a mass accretionrate of M =(2–4)×10−9M yr−1for a distance of 730 pc and1.15 kpc, respectively.We conducted high-resolution spectroscopy accompanied by

parallel multiband photometry to define the parameters of thedonor star and the binary as a whole. This study comes on theheels of observations of the object by the Kepler K2 mission.Results of 80 days of continuous, time-resolved photometry ofthe object are analyzed by Tovmassian et al. (2018, hereafterPaper I). Relevant to this follow-up article is the detection ofthe orbital period in the K2 light curve. In V1082 Sgr, there aredeep low states when the light curve appears to be dominatedby the donor star. Paper I concludes that such a light curvecannot be produced by an ellipsoidally deformed star because itwould create two dips per orbit, and hence the K star in thisbinary is not filling its Roche lobe. Instead, one dip per orbithas been observed, which was interpreted in Paper I as thepresence of a spot (cool, hot, or a combination of both) on thesurface of the donor star.In this paper, we approach the same problem from a different

point of view to confirm that V1082 Sgr is indeed a detachedbinary. In Section 2, we describe our observations ofV1082 Sgr and the corresponding data reduction. In Section 3,we present the analysis of a complex of absorption lines and themeasurements of radial velocities (RVs). The deduction ofrotational velocity is in Section 4, and the binary systemparameters are presented in Section 5. In Section 6, we reviewthe new information gathered from the emission-line profiles.We provide a discussion of the obtained results and theirapplication in Section 7.

2. Observations

The high-resolution spectroscopic observations ofV1082 Sgr were obtained using the echelle REOSCspectrograph (Levine & Chakarabarty 1995) at the 2.1 mtelescope of the Observatorio Astronómico Nacional at San

The Astrophysical Journal, 869:22 (10pp), 2018 December 10 https://doi.org/10.3847/1538-4357/aaec02© 2018. The American Astronomical Society. All rights reserved.

1

Pedro Mártir (OAN SPM),7 Mexico. The echelle spectrographprovides spectra covering the ∼3500–7105Å range with aspectral resolving power of R≈18,000. A total of 42 echellespectra were obtained during 11 consecutive nights in 2017July. A Th-Ar lamp was used for wavelength calibration. Thespectra were reduced using the echelle package in IRAF.8

Standard procedures, including bias subtraction, cosmic-rayremoval, and wavelength calibration were carried out using thecorresponding tasks in IRAF. The flux calibration is notoriouslydifficult with echelle spectra, which we did not attempt. Wemerged all orders after normalizing them to the continuum. Inthe overlapping regions, spectra were weighted according totheir signal level, and the ends of the orders were apodized witha cosine bell to prevent discontinuities. These merged spectrawere used for the spectral class and rotational velocitydetermination. There is a problem with the focus of theREOSC spectrograph, originally designed for photographicplates but now modified for a CCD camera that provides alarger field of view, and the focus deteriorates toward the endsof the spectral orders.

A number of K stars of different spectral and luminosityclasses of known rotational velocities used routinely asstandards (Fekel 1997) were observed along the object.HD 182488 was primarily used for rotational velocity measure-ments, together with HD 166620 for RV measurements.Several others of earlier and later spectral types, as well asluminosity class IV, were observed and used for spectral classdetermination. The log of observations is given in Table 1.

Multicolor photometric observations were obtained with theReionization and Transients InfraRed (RATIR), a simultaneoussix-filter imaging camera (r i Z Y J, , , , , and H bands) mountedon a Harold L. Johnson 1.5 m telescope at OAN (Butler et al.2012; Watson et al. 2012). It operates in robotic mode and isavailable in the absence of gamma-ray bursts alerts. We askedfor sequences of multicolor exposures prior, during, and afterthe spectral observations. The telescope is not designed forprolonged monitoring or long exposures, and the guiding isvery poor. Hence, the reduction of the data was very arduousand required one-by-one inspection of all images, a largefraction of which turned out to be worthless as a result of bad

pointing or guiding. However, we could use the good data toproduce decent light curves in the V, J, and H bands and get agood idea of the luminosity state of the object duringspectroscopic observations. The images were processed usingan automatic pipeline package for bias subtraction, flat-fielding,and cosmic-ray removal. The reduction pipeline also permitssky subtraction when necessary and astrometric alignment ofimages. For the latter, astrometry.net9 software was used.After these preliminary steps, we measured the magnitudes

of the object and of several similar and brighter comparisonstars found in the field using the IRAF task apphot within theDAOPHOT package. We used a circular aperture with 5 5radius for the object and comparison stars. The objectmagnitudes were then determined in a differential photometrywith comparison stars of known magnitudes. We checked thecomparison stars against each other to ensure that none of themwere variable and determined errors of measurements as astandard deviation.

3. Analysis of Absorption Lines

The spectrum of V1082 Sgr shows absorption lines from theK donor star throughout the wavelength range covered by ourdata set. Often the continuum is contaminated by the accretion-fueled radiation taking place in this system, as well as byemission lines of hydrogen and helium. However, as wasalready mentioned above, V1082 Sgr undergoes low-stateepisodes, when the contribution of the donor star is over-whelming. There appear to be brief intervals when the accretionstops completely, exposing pure K-type spectrum in the opticalrange. Tovmassian et al. (2016) demonstrated examples of suchspectra and suggested a K2 spectral class. In the new, high-resolution observations, we caught the system in the deepminimum, but it was too faint to get a good signal-to-noise ratio(S/N) spectrum with the echelle spectrograph. However, forthe analysis of absorption lines and their profiles, the spectraobtained in a higher-luminosity state are fine, since absorptionlines are better exposed on the background of the elevatedcontinuum. In Figure 1, the spectral exposures are marked atthe bottom of the light curve obtained by RATIR in near-IRfilters. The brightness of the system constantly changes withthe S/N at the continuum, reaching ∼20 in the single brightestspectra and about 2 in the faintest phase.

3.1. Spectral Type and RVs

Measurements of RVs improved greatly compared topreviously available data (Thorstensen et al. 2010; Tovmassianet al. 2016). We cross-correlated the ranges of spectracontaining multiple strong absorption features with referencespectra of standard stars. We used spectra of HD 182488(K0 V) and HD 166620 (K2V), which were observed with thesame instrumental settings together with the object, and asynthetic spectrum of Teff=5000 K taken from the BLUEREDdatabase (Bertone et al. 2008). We refined the orbital period byanalyzing the new RV measurements in combination with theprevious data (Tovmassian et al. 2016) for a longer time base.We fitted the RV curve using only data from high-resolutionobservations by fixing the period obtained from a largerdatabase. The differences in the results obtained using differenttemplates are negligible. Formal errors of measurements are

Table 1Log of Spectroscopic Observations Obtained with the

2.1 m Telescope and the Echelle Spectrograph

Date UT JD texp Numberyyyy mm dd 2,450,000+ (s) of Spectra

2017 Jul 07 7941 1200 12017 Jul 08 7942 1200 22017 Jul 10 7944 1800 12017 Jul 11 7945 1200 22017 Jul 12 7946 1200 22017 Jul 13 7946 1200 22017 Jul 14 7948 1200 82017 Jul 15 7949 1200 72017 Jul 16 7950 1800 82017 Jul 17 7951 1800 72017 Jul 18 7952 1800 2

7 http://www.astrossp.unam.mx8 IRAF is distributed by the National Optical Astronomy Observatories,which are operated by the Association of Universities for Research inAstronomy, Inc., under cooperative agreement with the National ScienceFoundation.

9 http://astrometry.net

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smaller by a factor of ∼2 in the case of the synthetic spectrum,although the residuals are similar for either case (only ∼10%smaller). The RV measurements are included in electronictables accompanying the paper.

The results of all measurements are summed up in Figure 2and Table 2. The parameters listed in the table are time ofprimary conjunction, center-of-mass velocity, velocity ampl-itude, orbital period, and standard deviation of residuals. Theorbit was assumed to be circular.

In order to produce a high-S/N spectrum of the donor star,we proceeded as follows. First, we corrected the Dopplerdisplacement of each merged spectrum according to themeasured RV of the absorption lines. Then, we estimated thelight contribution of the donor star by comparing the spectral-line intensities with those of a standard star. More precisely, wecalculated the multiplying factor minimizing the differencebetween the object spectrum and the scaled reference spectrumin four small selected spectral regions and then averaged thefour values into a single scale factor for each spectrum.Typically, the scale factors range from 0.25 to 0.6 dependingon the luminosity state of the object, as reflected in the lightcurve presented in Figure 1.

Then the lines of the donor star were removed from eachspectrum to measure the noise and identify deviant pixels to beremoved. The individual spectra corrected for RV, after beingscaled and cleaned, were combined to produce an averagespectrum. In this calculation, we used optimal weights thatwere calculated from the scale factors and the measured noise.

We compared the combined averaged spectrum with referencespectra of different spectral types. We selected from the Simbaddatabase10 stars in the temperature range 4500–5500K with solar

metallicity (0.0± 0.1 dex) and surface gravity corresponding tomain-sequence stars (log g=4.3–4.6). Then we downloadedfrom the ESO archive11 high-S/N ( >S N 200) spectra of theseobjects taken with the HARPS spectrograph.The selected stars are listed in Table 3.Finally, we built spectral templates by combining some of

these spectra and convolving them with an appropriaterotational profile (25 km s−1) and scaled by a factor of 0.5 inorder to make them consistent with that of V1082 Sgr, whoselines are reduced by the light contribution from the companion.The final templates were T4660 (HD 131977), T4900 (averageof HD 160346 and HD 23356), T5080 (HD 192310, HD22049), T5250 (HD 149661, HD 165341), and T5430 (HD69830, HD 152391).We looked for metallic lines that can be used for spectral-

type classification in the spectral regions less contaminated bythe companion. Figure 3 shows the spectrum of V1082 Sgr in

Figure 1. Light curve of V1082 Sgr in three bands during the spectroscopicobservations. In the bottom panel, measurements of IR observations areplotted. Epochs of spectral exposures are marked in the bottom of the panel. Inthe bottom left corner, the photometric error error bar is indicated. The V-bandlight curve is presented in the middle panel. In the top panel, color indexes arepresented. All photometric bands and color indexes are plotted in distinctcolors and indicated on the right sides of the light curves. The horizontal dottedlines in the top panel indicate colors corresponding to a K2 main-sequence star.

Figure 2. The RV curve of the donor star measured by cross-correlation withthe synthetic spectrum. Systemic velocity is marked with a dotted line. Theparameters of the average fit are presented in Table 2.

Table 2Parameters of the RV Curve

T0 HJD 2,457,939.161±0.002Vγ km s−1 51.8±0.6Kd km s−1 45.3±0.7P days 0.867525±0.000015σ km s−1 2.8

10 http://simbad.u-strasbg.fr/simbad/sim-fsam 11 http://archive.eso.org/wdb/wdb/adp/phase3_spectral/form

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comparison with the reference spectra. Some V I-to-Fe I andCr I-to-Fe I line ratios are sensitive to temperature. Anothergood indicator is the aspect of the λ4227 Ca I line. In all cases,the line ratios suggest a spectral type of K2 V (templates T4900to T5250).

The surface of the donor is likely to have spots, similar to thechromospherically active stars (Berdyugina 2005), so thetemperature measurements vary with orbital phase (e.g.,Watson et al. 2007). It is clear from the spectrum that thedonor star in V1082 Sgr is not a giant star, but whether thespectrum corresponds exactly to a normal-size main-sequencestar or is slightly larger is hard to tell from the spectral features.We are inclined to identify the donor star of V1082 Sgr asK1 V–K2V. The high-resolution spectra thus confirm theresults obtained previously by Tovmassian et al. (2016) butmake the classification more reliable.

4. Rotation

The Kepler K2 mission 80 days of continuous photometryshows that the orbital period is present in the light curve duringthe low state (Paper I). The period appears as a smooth, nearlysinusoidal, single-humped wave during a deep minimum whenthe optical flux is produced predominantly by the K star. Theobserved light curve is interpreted as evidence that the K star isnot deformed by overflowing its Roche lobe but has a spot orspots on its surface, reflecting its rotational period. Since therotation can be safely assumed to be synchronous, the projectedrotational velocity can give information about the radius of thelate-type stellar companion. In a first trial, we determine v isinusing the method developed by Díaz et al. (2011), which allowsus to deal with the line blending present in late-type stars. Thistechnique reconstructs the rotational profile from the cross-correlation function of the object spectrum against a sharp-linedtemplate and derives the rotational velocity from the first zeroof the Fourier transform (FT) of the rotational profile. In thesecalculations, we adopted limb-darkening coefficients fromNeilson & Lester (2013).

Measuring the rotational velocity is a difficult task for thisobject. Several factors conspire against a reliable determina-tion. Díaz et al. (2011) mentioned that the method workssatisfactorily when the rotational broadening is larger than theinstrumental profile (or other broadening effects) by a factorof 2. In the present case, the rotational broadening ( »v isin27 km s−1) is relatively low in comparison to the spectralresolution (the FWHM of the instrumental profile is about18–20 km s−1). On the other hand, the S/N is modest (∼20 forindividual observations, ∼80 for the average spectrum), which

is aggravated by the dilution of the spectral lines due to thelight contribution of the companion.Finally, the useful spectral regions are rather limited, since

regions contaminated by the companion emission lines must beexcluded, as well as those containing the strongest lines of thelate-type star itself, since such line profiles are affected bypressure broadening. Some examples of the power spectra ofthe line profiles are shown in Figure 4.We applied the mentioned technique to a few selected

regions presented in the bottom part of Figure 4. In the bestthree regions, we obtained vsini=27.7±1.0, 27.6±2.5,and 26.3±1.5 km s−1, while some others failed to define areliable zero FT at all.As a second strategy, we estimated v isin by comparing the

target spectrum with a template previously convolved withdifferent rotational profiles. We used as a reference theobserved spectrum of HD 182488, which was convolved withrotational profiles between 22 and 32 km s−1. The comparisonwas done by cross-correlating each spectrum against theoriginal reference spectrum and measuring the FWHM of thecentral peak of the cross-correlation function. The rotation ofthe reference star is below the spectral resolution and has anegligible contribution to the peak FWHM.The main advantage of this method with respect to the

former is that the contribution of the instrumental profile is lesscritical. Particularly, the mentioned problem of deficient focusover the CCD (variable instrumental profile along thespectrum) is largely mitigated by the fact that both object andreference spectra are taken under the same conditions and,therefore, are affected in the same way. Hence, we consideredthis strategy more reliable and applied it to 10 spectral regionsranging from 4250 to 6450Å. We used as a template thespectrum of HD 182448 (a sharp-lined K0 V star) taken withthe same instrument. It is probably slightly hotter than theobject, and their chemical abundances do not match exactly.However, the very low =v isin 0.6 km s−1 rotational velocityof the template and variety of lines used for measurementsmake it suitable for the task.We also considered the effect of velocity smearing on our

measurements as an outcome of relatively long exposure times(1200 s) used in observations. We convolved a syntheticspectrum representing the intrinsic stellar spectrum (with

=v isin 26.5 km s−1) with boxy kernels of widths equal tothe RV variation during the exposure time. We calculated themean spectrum and measured the rotation with the sameprocedure as described in this section. The results showed thatour measurement of v isin would be about 0.3 km s−1 abovethe true value, that is, well below the uncertainties cited below.The obtained values of v isin average 25.3±2.4 km s−1

within a small error spread. However, for three regions below4900Å,the values are slightly smaller and show a tendency todecrease toward shorter wavelengths. The contribution of thedonor star at shorter wavelengths drops rapidly when the objectis not in deep minima, hence the measurements at the blue endof the spectra are less reliable. Excluding these three values, weobtain = v isin 26.5 1.4 km s−1 of a very stable subsample.Considering the possible differences in the instrumental

profile between the observations of the object and referencestar, we adopted a value of 26.5±2.0 km s−1 for the projectedrotational velocity of the donor companion. Either method hasits uncertainties and limitations, and the statistically derived

Table 3List of Stars Used to Produce Templates

Star Teff log g Met SpType

HD 131977 4669 4.29 −0.04 K4 VHD 160346 4871 4.51 +0.00 K3 VHD 23356 4924 4.55 −0.08 K2.5 VHD 192310 5077 4.50 +0.04 K2 VHD 22049 5090 4.55 −0.07 K2 VHD 149661 5254 4.54 +0.03 K1 VHD 165341 5260 4.51 +0.00 K0 VHD 69830 5396 4.47 −0.05 G8 VHD 152391 5467 4.49 −0.02 G8 V

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error bars are probably underestimated, but matching results ofindependent measurements assure us that the result is realistic.

5. Stellar Parameters

If we assume that the rotation of the K-type star (markedwith subindex “d” for “donor”) is synchronized with the orbitalmotion, the relative radius of this star can be written as

=+( )

· ( )R

a

q

q

v i

K1

sin, 1d d

d

where =q M Mwd d is the mass ratio. On the other hand,according to Eggleton (1983), the effective radius of the Rochelobe in units of the orbital semiaxis can be calculated throughthe expression

=+ + -· ( )

( )R

a q q

0.49

0.6 ln 1, 2L

2 3 1 3

which is better that 1% for any value of the mass ratio.12

From these two equations, we obtain the ratio between thestellar radius and the critical radius:

=+ +

+

-

-

⎛⎝⎜

⎞⎠⎟ · [ ( )]

( )( )R

R

v i

K

q q

q

sin 0.6 ln 1

0.49 1. 3d

L

d

d

2 3 1 3

1

The first factor is known from the spectroscopy:= ( )v i Ksin 0.586 0.045d d . Then, the constraint imposed

by the Roche lobe on the donor star volume ( R Rd L)provides an upper limit for the mass ratio: q�1.42±0.2.

Fortunately, we have strong constraints on the mass of thecompact companion from the X-ray spectroscopy. Bernardiniet al. (2013) derived a WD mass of Mwd=0.64±0.04M by

modeling the spectrum obtained by XMM-Newton EPIC andSwift BAT.For a comprehensive analysis of the possible configurations,

we calculated a, Md, Rd, and RL for different possible values ofq. More precisely, from Mwd and q, we calculated the mass ofthe donor star Md and the total mass, and from the Keplerequation, we calculated the orbital semiaxis. Then the radii ofthe donor Rd and its Roche lobe RL were calculated fromEquations (1) and (2).The results are shown in Figure 5. The radius of the donor

star Rd is plotted as a function of Md with a blue line; bluedashed lines mark the uncertainty interval of the radius due tothe error in v isin . The radius of the Roche lobe correspondingto the donor star is plotted with a violet line.The adopted solution is marked in Figure 5 by a black dot.

The full solution of the binary system parameters issummarized in Table 4. The consigned uncertainties have beencalculated taking into account the observational errors in Porb,v isind , Mwd, and Kd and the error of Md, which has beenestimated from the spectral type (see Figure 5).Thus, the donor fills only a fraction of its Roche lobe (about

one-third of the corresponding volume), although it issignificantly (∼70%) larger than a nonevolved main-sequencestar of the same mass. In fact, the evolution of stars of suchmasses is so slow that this mass–radius relation can beexplained only as the result of a nonstandard evolution.

5.1. Stellar Parameters: Gaia Distance

While this paper was in the final stages of preparation, thesecond Gaia data release (Gaia DR2; Gaia Collaboration et al.2016), which provides precise parallaxes for an unprecedentednumber of sources, became available. According to Gaia DR2,the distance to V1082 Sgr is 669±13 pc. This allows us toimpose direct and stringent limits on the size of the donor star.

Figure 3. Comparison of the spectral morphology of V1082 Sgr with reference spectra of different spectral types. HD 182488 (K0 V), HD 142980 (K1 IV),HD 115404 and HD 166620 (averaged as K2 V), and HD 219134 (K3 V) were observed along with V1082 Sgr during the same period of observations.

12 In the original formula by Eggleton, we have changed q to -q 1, since in hiswork, the mass ratio is M Md wd.

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Using the faintest visual magnitude V=14.8, repeatedlyrecorded during deep minima in over 1500 days; interstellarreddening of -( )E B V =0.15 (Schlegel et al. 1998); andTeff=4930 K, a temperature corresponding to a K2-type star,we obtain Rd=1.165 R. If we take into account theuncertainty in temperature of up to 350 K, which is the largestfactor affecting the luminosity, we obtain a range of values ofthe donor star Rd=1.03–1.34 R, independent of the mass ofthe binary components. This range of values is marked inFigure 5 as a horizontal strip within dash-dotted green lines,with the central value exactly corresponding to what wededuced before the distance was known.

6. Analysis of Emission Lines

From the previous lower-resolution spectroscopy, it wasknown that the emission lines are single-peaked and fairlysymmetric (Tovmassian et al. 2016). However, measuringemission lines in the low-resolution spectra as a single line hasbeen producing RVs of low amplitude and a huge scatter ofpoints that was not the result of measurement errors. Theamplitudes and phases of different emission lines were vastlydifferent too, indicating that the situation was not assessedcorrectly.

At higher resolution, the profiles of lines appear to be not assymmetric as was thought, and we made an attempt to discernthem into two components. The attempt was particularlysuccessful in the case of the He II λ4685.75 line, which issomewhat sharper than the Balmer lines. We first used thedeblending option of the IRAF splot procedure to fit eachprofile with two Gaussians. For each spectrum, we obtained apair of RV values corresponding to two components. By eyeinspection, we selected one component per spectrum thatappeared to belong to a sinusoidal pattern in the RV–versus–orbital phase diagram. It was not possible to identify the rightcomponent in every spectrum, but in more than half of thecases, the selected points formed a clear pattern that could be fitwith a sine curve with the orbital period. We calculated thecentral wavelength of that component for each spectrum anditerated the deblending procedure for all spectra, this timekeeping one component’s central wavelength fixed and anotheras free. We also set the FWHMs of both Gaussians as freeparameters. The measurements of the second componentformed a periodic pattern too, reasonably well fitted withanother sinusoid. Finally, we did a third iteration of deblendingby fixing the central wavelengths of both components

Figure 4. The FT of the autocorrelation function between the selected regionscontaining absorption lines and the template is presented in the top panel. Thefirst zero of the FT corresponds to the rotational velocity (see Díaz et al. 2011for details). The selected spectral regions are plotted in the bottom five panels.The FT power of each region is plotted with a corresponding color.

Figure 5. Mass–radius diagram for the donor star in V1082 Sgr. The black dotrepresents our best solution. The blue line (with limits marked as dashed lines)is the solution from the dynamical constraints. The violet line is the Roche lobesize. The green line is the radius of the donor star determined by the distancemodulus The limits mark an error strip related to the temperature ambiguity(dash-dotted lines). See text for explanation.

Table 4Deduced Absolute Parameters of V1082 Sgr

Parameter Units Value

Md M 0.73±0.04Mwd M 0.64±0.04i deg 23.3±1.3q 0.88±0.09a R 4.25±0.07Rd R 1.16±0.11RL R 1.66±0.05

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according to the calculated sinusoids and leaving the FWHMand intensities variable. We obtained excellent fits to the lineprofiles in most of the cases. In only 10 spectra out of 38, theprogram could not find two emission components withreasonable parameters.

In order to separate emission lines into two components, weassumed that they move sinusoidally. We defined the mostreadily identifiable component and then refined the parametersof the other one. Of course, this is a very idealistic approach;the reality has to be much more complicated, because the gasstreams producing emission lines have intrinsic velocities anddirections not coinciding with the orbital motion.

The RV measurements of these two components are plottedagainst the orbital phases in the bottom panel of Figure 6. Thepoints correspond to the calculated central wavelengths thatwere fixed in the last deblending attempt; hence, they formperfect sinusoids. The orbital phases are calculated according tothe ephemeris determined by absorption spectra. In the middlepanel of Figure 6, the FWHMs of both components are plotted.Most are very consistent with the general trend. Some stronglydeviate, indicating problems usually related to the phases inwhich both components crisscross and become indistinguish-able. In such a case, the program tends to pick a broad secondcomponent extending to the noise in the continuum or use anabsorption component. Such cases appear as points above thedotted line corresponding to zero in the top panel of Figure 6,which depicts the equivalent weights (EWs) of the components.Those points in the plot are marked by red crosses. Amongthem are also some points that have large FWHM, inconsistentwith the average.

In Figure 7, examples of line profile fits are presented. Weomitted orbital phases (marked by numbers in each panel) inwhich the lines were not split into two components correctly,with one component being in absorption. In the other case, oneof the components is getting too wide, like in phases f=0.47and 0.58, as a consequence of both of them getting too closeand difficulty in separating them. Although the procedure ofselecting components and fixing central wavelengths is some-what arbitrary, the final result is encouraging. Both componentsshow larger RV amplitudes than the entire line when measuredwith a single Gaussian.The component marked in red in Figures 6 and 7 maintains a

rather stable FWHM throughout all orbital phases. Neithercomponent appears to vary strictly in antiphase from theabsorption line. Neither it is expected to be related to the stellarelements of the binary. Invalid points constitute a quarter of allmeasurements and do not influence the general interpretation.We assume that the emission lines are produced by the

ionized gas between the stellar components. The linespractically disappear when the accretion is halted and thesystem is in a deep minimum. Hence, we do not have RVmeasurements for the first 3 nights, when the lines were faint orabsent. After the accretion is reestablished, the disentangledcomponents of the He II line act similar to polars, showingphase shifts and high velocities related to the stream intrinsicvelocity rather than the orbital velocity. The brightness of theobject varies significantly in very short timescales (Paper I),and the intensity of the lines changes accordingly.In an attempt to better understand the components of the

emission lines, we used Doppler tomography. The system has arather small inclination for sensible tomograms to be made.Observed lines or their components of variable intensity andwidth make the reading of tomograms impossible. Hence, wemade artificial lines of fixed FWHM and intensity with RVsand phases of the real components. The FWHM was fixed at 5and 7.5Å for the lower- and higher-velocity components,respectively, according to their averages. We also added anartificial narrow (FWHM=0.7Å) absorption line emanatingfrom the secondary to make the Doppler map more illustrative.Doppler maps of these three lines are presented in Figure 8.The inclination angle and masses derived from observationsand listed in Table 4 were used to plot the Roche lobes and starlocations on the Doppler map.The intensity of the lines is not irrelevant, but since there is

no well-established pattern of line intensity and FWHM changewith the phase, we kept them constant in all cases. The artificialspectra were distributed unevenly by phases, according toobservations. Hence, the spots on the map are not ideallyround. One has to bear in mind that this image is simplistic andmay not reflect the complexity of ionized gas distribution in thebinary.The Doppler map illustrates where in the velocity coordi-

nates the lines originate. The high-velocity emission comp-onent is concentrated in the third quadrant. It may correspondto the accretion curtain component observed in polars asdescribed by Heerlein et al. (1999; see their Figure 5). Theballistic component is obviously absent; instead, we have alower-velocity component in the first quadrant, practicallybetween the stars. This component may originate in thegas flowing along the coupled magnetic lines (magneticbottleneck).

Figure 6. Parameters of two components of emission-line He II marked by redsquares and blue circles. The RVs are presented in the bottom panel, theFWHMs in the middle panel, and the EWs in the top panel. Three iterations ofthe deblending procedure were made to find solutions that correspond to twocomponents with strictly periodical RVs. The central wavelengths, FWHMs,and core intensities of these components were used to produce the profilesshown in Figure 7. The horizontal dotted line in the top panel corresponds tozero. Points above that line are invalid and marked with crosses. Also markedwith crosses are the points with extremely broad components, as can be seen inthe middle panel.

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Parsons et al. (2013) detected similar line components(corresponding to the magnetic bottleneck) in a detachedbinary, but with an M-type donor star. The RV and phasing ofthe fainter of two components of Hα that they observed indicatethat it comes from gas located between the stars.

To pinpoint the donor star on the tomogram, we use thesimulated absorption line. The absorption line produces a spot

in the tomogram corresponding to the center of mass of theK star.

7. Discussion and Conclusions

We conducted high-resolution spectroscopy of V1082 Sgr,proposed to be one of two possible candidates for a pre-polarwith an early-K-type donor star (Tovmassian et al. 2017). Thisspectroscopic study was accompanied by prior continuous, 80day photometry of the object by the Kepler K2 mission. Theresults of the photometry are reported in a separate publication(Paper I). For a wholeness of argument, we must repeat themain conclusion of Paper I: the orbital modulation detected inthe light curve of V1082 Sgr persists during the deep minima,when the donor star is the predominant source of light. It isargued that the variability is caused by spots on the surface(either hot, cold, or a combination of both). No double hump isdetected in the light curve. Hence, it is concluded that the donorstar is not ellipsoidal and that it rotates with the orbital period.By measuring the rotational velocity of the donor star, we cango a step further and estimate other important parameters of thebinary system.These parameters are listed in Table 4. According to them,

the donor star occupies about 70% of its corresponding Rochelobe radius, nevertheless exceeding the main-sequence star sizeof similar temperature. This means that the donor star hasprobably departed from the zero-age main sequence.These estimates and conclusions are based on the assump-

tion that the WD in this detached binary accretes as a polar andhas a rather average mass for a WD according to the spectrumof the X-ray emission.While there is no direct evidence of an MWD, it is obvious

that the donor star is magnetically active and has large spot(s)on its surface. A possible explanation of the mass transfer andaccretion on the WD is the magnetic coupling, capture of thestellar wind from the donor star, and channeling (siphoning) of

Figure 7. Examples of disentangling emission-line He II into two components, plotted by red and blue dotted lines. Black curves correspond to the sum of the twocomponents, while the observed spectra are plotted in light violet. The vertical axes are in normalized counts, with a continuum corresponding to one unit. Thenumbers in each box indicate the orbital phase at which that spectrum was taken.

Figure 8. Doppler maps of an absorption line and two components of He IIemission. All lines are artificially made with RVs of measured lines andaverage FWHM and intensities. The image map corresponds to the donor star,while the higher-velocity (blue) and lower-velocity (red) components arepresented in the form of isochrones. The Roche lobes and stellar position aremarked according to Table 4.

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the matter onto the magnetic pole of the WD. Doppler maps ofthe He II line, which consists of two components, testify thatthe ionized gas is not emitting from areas and spots associatedwith the accretion disk or streams proper to ordinary polars.This has been observed already in compact binaries comprisedof an MWD and an M-type star (Parsons et al. 2013) for whichthe pre-polar phenomenon is well established. However,significant differences may appear if the binary contains anearlier spectral-type donor star.

These differences are related to the fact that a more massivedonor star has a large convective envelope with intensechromospheric activity, has a higher-rate stellar wind, and isprone to evolution in a Hubble time, unlike M-dwarfcompanions. The separation of the binary is also larger, andthe mass ratio is reversed (as compared to pre-polars with Mcomponents or CVs), making the Roche lobe of the donor starmuch bigger than the size of a main-sequence star and henceproviding a long time for evolution until the binary becomessemidetached.

There is a lack of knowledge regarding stellar winds ingeneral and their dependence on rotational velocity due to thelarge spread in rotation rates of isolated stars at young ages.However, the latest models predict that the mass-loss rate dueto the stellar wind depends moderately on the mass of low-mass stars and more significantly on the rotational velocity(Johnstone et al. 2015 and references therein). Most of theobservational studies of mass loss by stars of solar mass andbelow presume that the rotation slows down because ofmagnetic braking and the diminishing stellar wind. Wood et al.(2002) estimated that at younger ages, the solar wind may havebeen as much as 103 times stronger. This enables a steepincrease of the mass-loss rate estimate from the fast-rotatingdonor star in V1082 Sgr compared to identical single stars.Chromospheric activity and a larger surface area can furtherfuel the mass loss. The mass-loss rate appears to depend on theX-ray surface flux as a power law (Wood et al. 2002).

The X-ray flux from V1082 Sgr in the minimum is probablydue to the donor star, while the accretion on the WD is halted.The flux matches an upper limit observed from similarmagnetically active stars. Thus, all prerequisites exist to expecta mass accretion rate a few orders higher than that in pre-polarswith an M-star companion.

Another thorny issue is how mass loss from the donor starconverts into mass accretion on the WD. Cohen et al. (2012)demonstrated that matter lost through the stellar wind will notalways find its way to the WD. There are configurations inwhich all the wind can effectively siphon to the MWD.Curiously, such configurations require antialigned and rathermodest magnetic fields. However, it is still incomprehensiblehow the accretion rate reaches an estimated 2×10−9M yr−1

(Bernardini et al. 2013) in V1082 Sgr. With the Gaia distance,this rate is 1.3 times less but still of the same order.

The accretion is not continuous, however. It is regularlyinterrupted by deep minima states where there is no evidence ofaccretion at all. We speculate that the cessation of accretion isrelated to the broken magnetic coupling. The deep minima lastonly a few orbital periods, then accretion is restored.

Such a high accretion rate exceeding that of an ordinary CVis unusual and raises questions about how it will affect theevolution of the binary system. The excess nitrogen abundanceprobably indicates that V1082 Sgr has formed from massiveprogenitors and underwent an episode of thermal timescale

mass transfer, as was pointed out by Bernardini et al. (2013 andreferences therein).We found independent observational evidence suggesting

that V1082 Sgr is a detached binary containing a slightlyevolved early-K star. If this proposition is correct, we see noalternative to magnetic coupling as the means of transferringmatter and angular momentum from the donor to an MWD.This object corroborates the existence of pre-polars with earlierspectral-type donor stars. It offers an explanation as to whymagnetic systems are not found in the search for WD+FGKdetached binaries (Parsons et al. 2016; Rebassa-Mansergaset al. 2017). Yet the object presents certain challenges. It isnecessary to estimate the magnetic field strength of the WD andits temperature and mass directly by UV observations.Furthermore, it is necessary to calculate possible evolutionscenarios in conditions of a high mass transfer rate while thesystem is still detached and in which way it will evolve.

This paper has made use of data obtained from the ESOScience Archive Facility under request numbers 360705,360734, 361117, and 360635. This work has made use of datafrom the European Space Agency (ESA) mission Gaia(https://www.cosmos.esa.int/gaia), processed by the GaiaData Processing and Analysis Consortium (DPAC). Fundingfor the DPAC has been provided by national institutions, inparticular the institutions participating in the Gaia MultilateralAgreement. DGB is grateful to CONACyT for grants allowinghis postgraduate studies. M-SH is supported by the DoctoradoNacional CONICYT 2017 folio21170070, and JVHS issupported by a Vidi grant awarded to N. Degenaar by theNetherlands Organization for Scientific Research (NWO). GTand SZ acknowledge PAPIIT grants IN108316/IN-100617 andCONACyT grant 166376.Facility: OAN SPM.

ORCID iDs

G. Tovmassian https://orcid.org/0000-0002-2953-7528

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